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Equation 4 · Part 10 · Comparing the Main Approaches to Origins of Life and Astrobiology

Denominator: P(D mid H_bio) P(H_bio) + P(D mid H_ab) P(H_ab)

P(Hbio∣D)=P(D∣Hbio) P(Hbio)P(D∣Hbio) P(Hbio)+P(D∣Hab) P(Hab)P(H_{bio} \mid D) = \frac{P(D \mid H_{bio})\, P(H_{bio})}{P(D \mid H_{bio})\, P(H_{bio}) + P(D \mid H_{ab})\, P(H_{ab})}
P(D∣Hbio) P(Hbio)+P(D∣Hab) P(Hab)P(D \mid H_{bio})\, P(H_{bio}) + P(D \mid H_{ab})\, P(H_{ab})

What this part means

The complete quantity below the fraction bar; it must be nonzero for this division.

Its job in the formula

P(D mid HbH_bio) P(HbH_bio) + P(D mid HaH_ab) P(HaH_ab) occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

The passage around this formula

What lets these three very different kinds of evidence be compared at all is a shared logical structure that the Astrobiology community has tried to formalize explicitly rather than leave implicit. David Catling and coauthors proposed treating a biosignature detection as a Bayesian inference problem: a prior probability that a given planet or sample harbors life, updated by the likelihood of the observed data under a “life” hypothesis versus under one or more specific abiotic alternative hypotheses, yields a posterior probability rather than a binary yes-or-no verdict [ 7 ] . Written compactly, for a single candidate abiotic alternative HabH_{ab} competing with a life hypothesis HbioH_{bio} given…

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

Open the illustrated fractions: division written vertically guide →

Sources cited in the surrounding passage

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